Real-Time FPGA-Based Analytical Space Harmonic Model of Permanent Magnet Machines for Hardware-in-the-Loop Simulation

This paper presents a real-time analytical space harmonic model of permanent magnet synchronous machines with shaped poles. The goal of this configuration is to produce an air-gap flux density distribution as close to sinusoidal as possible to enhance the machine performance. The analytical model is derived to predict the magnetic fields and the machine behavior by solving Maxwell's equations and applying the superposition theorem. The digital hardware realization of the model is developed on the field-programmable gate arrays (FPGAs) in a paralleled and pipelined paradigm for an efficient hardware design. Such real-time emulation on FPGA can be used in the design procedure and the assessment of newly prototyped controllers and drive systems in the hardware-in-the-loop platform. In this paper, the analytical model of the machine is simulated in real time on 7.5 ns input FPGA clock cycles, and the achieved executive time is 1.8 ${\mu }\text{s}$ . The captured real-time analytical results demonstrate the good accuracy of the emulator in comparison with the offline 2-D time-stepping transient finite-element solution obtained by JMAG software.